Question: What do the following two equations represent? $-4x+y = 4$ $-4x-16y = 4$
Answer: Putting the first equation in $y = mx + b$ form gives: $-4x+y = 4$ $y = 4x+4$ Putting the second equation in $y = mx + b$ form gives: $-4x-16y = 4$ $-16y = 4x+4$ $y = -\dfrac{1}{4}x - \dfrac{1}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.